Thermodynamics HW Solutions 307

Thermodynamics HW Solutions 307 - k o = = ° ° = ( )( . )...

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Chapter 4 Transient Heat Conduction 4-34 An egg is dropped into boiling water. The cooking time of the egg is to be determined. Assumptions 1 The egg is spherical in shape with a radius of r 0 = 2.75 cm. 2 Heat conduction in the egg is one-dimensional because of symmetry about the midpoint. 3 The thermal properties of the egg are constant. 4 The heat transfer coefficient is constant and uniform over the entire surface. 4 The Fourier number is τ > 0.2 so that the one-term approximate solutions (or the transient temperature charts) are applicable (this assumption will be verified). Properties The thermal conductivity and diffusivity of the eggs are given to be k = 0.6 W/m. ° C and α = 0.14 × 10 -6 m 2 /s. Analysis The Biot number for this process is Bi hr
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Unformatted text preview: k o = = ° ° = ( )( . ) ( . ) . 1400 0 0275 0 6 64 2 W / m . C m W / m. C 2 Water 97 ° C Egg T i = 8 ° C The constants λ 1 and A 1 corresponding to this Biot number are, from Table 4-1, 9969 . 1 and 0877 . 3 1 1 = = A Then the Fourier number becomes 2 . 198 . ) 9969 . 1 ( 97 8 97 70 2 2 1 ) 0877 . 3 ( 1 , ≈ = ⎯→ ⎯ = − − ⎯→ ⎯ = − − = − − ∞ ∞ τ θ τλ e e A T T T T i sph Therefore, the one-term approximate solution (or the transient temperature charts) is applicable. Then the time required for the temperature of the center of the egg to reach 70 ° C is determined to be min 17.8 = = × = α τ = − s 1068 /s) m 10 14 . ( m) 0275 . )( 198 . ( 2 6 2 2 o r t 4-18...
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This note was uploaded on 01/19/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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